Can a person wtih alpha thalassemia trait donate blood?

Maybe. A person with Alpha thalassemia trait may be not anemic or mildly anemic. If he is not anemic, he can be a blood donor. However, since he has a more difficult time making hemoglobin (to make new red blood cells), he may not wish to be a blood donor.
Yes you can. The red cross will accept blood donations from you if you are not anemic which means that you have a hemoglobin of at least 12.5 or more . Your blood group may be a rare type and may help someone if needed .